%I #4 Mar 21 2013 04:42:16

%S 243,19759,2030665,216562815,23328902821,2519813048575,

%T 272386213374733,29451199763005655,3184571844145868835,

%U 344356382352508380215,37236420474777196695869,4026507614168634996035183

%N Petersen graph (3,1) coloring a rectangular array: number of nX6 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

%C Column 6 of A223504

%H R. H. Hardin, <a href="/A223502/b223502.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 171*a(n-1) -7597*a(n-2) +66978*a(n-3) +2583824*a(n-4) -51950940*a(n-5) -114768696*a(n-6) +9054636698*a(n-7) -36718682736*a(n-8) -634109162555*a(n-9) +4922415752542*a(n-10) +17684952456223*a(n-11) -257017179787974*a(n-12) +44697122178759*a(n-13) +6813950647173658*a(n-14) -14214676649780235*a(n-15) -95256883925367556*a(n-16) +349764223086150739*a(n-17) +638075361803414056*a(n-18) -4132669977915280075*a(n-19) -655758716192007656*a(n-20) +27891199596575003557*a(n-21) -19946115396154900446*a(n-22) -113398578310551386143*a(n-23) +153863761785049382215*a(n-24) +275337771685131610985*a(n-25) -574115913592410065960*a(n-26) -351972189331006256045*a(n-27) +1287605861871487083865*a(n-28) +49832950543007059662*a(n-29) -1835218083346443858712*a(n-30) +584632105931636070627*a(n-31) +1673748635702117796496*a(n-32) -1004898866351611047643*a(n-33) -943485141803302660797*a(n-34) +864920595743414931962*a(n-35) +287374596274394425107*a(n-36) -446718459459833923638*a(n-37) -15289668350134708829*a(n-38) +143310897427441778213*a(n-39) -21277189785541190392*a(n-40) -28130375346377645531*a(n-41) +8130899172562042318*a(n-42) +3152590800552865603*a(n-43) -1415161150801970578*a(n-44) -157323743807361158*a(n-45) +132817713592064303*a(n-46) -2466246093921598*a(n-47) -6544805823376510*a(n-48) +605341636474744*a(n-49) +143100794076816*a(n-50) -20407671803168*a(n-51) -733454285952*a(n-52) +152009496576*a(n-53)

%e Some solutions for n=3

%e ..0..2..1..0..2..1....0..1..0..1..4..1....0..1..0..3..0..2....0..2..0..3..5..3

%e ..0..2..1..0..2..1....0..3..4..1..4..1....0..1..0..2..0..2....0..2..0..2..5..3

%e ..0..2..1..0..2..0....0..3..4..5..4..1....0..1..0..2..0..3....0..2..0..3..5..3

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 21 2013